36q^2=6912

Solution for 36q^2=6912 equation:

36q^2=6912

We move all terms to the left:

36q^2-(6912)=0

a = 36; b = 0; c = -6912;
Δ = b2-4ac
Δ = 02-4·36·(-6912)
Δ = 995328
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{995328}=\sqrt{331776*3}=\sqrt{331776}*\sqrt{3}=576\sqrt{3}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-576\sqrt{3}}{2*36}=\frac{0-576\sqrt{3}}{72}
=-\frac{576\sqrt{3}}{72}
=-8\sqrt{3}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+576\sqrt{3}}{2*36}=\frac{0+576\sqrt{3}}{72}
=\frac{576\sqrt{3}}{72}
=8\sqrt{3}
$